Communications in Mathematical Physics

, Volume 225, Issue 3, pp 633–637

A Remark on Lp-Boundedness of Wave Operators¶for Two Dimensional Schrödinger Operators

  • Arne Jensen
  • Kenji Yajima

DOI: 10.1007/s002200100603

Cite this article as:
Jensen, A. & Yajima, K. Commun. Math. Phys. (2002) 225: 633. doi:10.1007/s002200100603

Abstract:

Let H=−Δ+V be a two dimensional Schrödinger operator with a real potential V(x) satisfying the decay condition \(\), δ > 6. Let H0=−Δ. We show that the wave operators \(\) are bounded in Lp(R2) under the condition that H has no zero resonances or bound states. In this paper the condition \(\), imposed in a previous paper (K. Yajima, Commun. Math. Phys. 208, 125–152 (1999)), is removed.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Arne Jensen
    • 1
  • Kenji Yajima
    • 1
  1. 1.Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan. E-mail: yajima@ms.u-tokyo.ac.jpJP

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